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At least three people have died and several more are believed to be missing after a boat carrying refugees from Turkey sank off the Greek island of Kalymnos, according to Authorities in Greece and Turkey.

The Greek coast guard said 15 people were rescued and one body was recovered after the wooden boat sank in mild weather conditions before dawn on Friday. Two other bodies believed to be from the same vessel were found by the Turkish coast guard.

In two other incidents early on Friday, 127 people were rescued from boats in distress near the Greek island of Chios.

Greece's government says an agreement last year between the European Union and Turkey to combat migrant trafficking is not in danger of collapsing, despite a strain in relations between the EU and Ankara.

Migrants who arrived on Greek islands after that agreement took effect in March 2016 are not allowed to travel to the mainland before their asylum claim has been examined — causing serious overcrowding at government-run camps.

"What's happening is that the EU-Turkey deal is only being half implemented, because the part that involves migrants being returned to Turkey is not happening," Chios Mayor Michalis Vournous told a parliamentary committee briefing in Athens on Thursday.

Vournous and other Greek island mayors said the government and the EU have delayed promised assistance to deal with the rising numbers of migrants.

"The situation must be alleviated on the islands for the sake of the local economy and local society. Island life needs to return to normal," he said.